Single hyperspectral image super-resolution (single-HSI-SR) aims to improve the resolution of a single input low-resolution HSI. Due to the bottleneck of data scarcity, the development of single-HSI-SR lags far behind that of RGB natural images. In recent years, research on RGB SR has shown that models pre-trained on large-scale benchmark datasets can greatly improve performance on unseen data, which may stand as a remedy for HSI. But how can we transfer the pre-trained RGB model to HSI, to overcome the data-scarcity bottleneck? Because of the significant difference in the channels between the pre-trained RGB model and the HSI, the model cannot focus on the correlation along the spectral dimension, thus limiting its ability to utilize on HSI. Inspired by the HSI spatial-spectral decoupling, we propose a new framework that first fine-tunes the pre-trained model with the spatial components (known as eigenimages), and then infers on unseen HSI using an iterative spectral regularization (ISR) to maintain the spectral correlation. The advantages of our method lie in: 1) we effectively inject the spatial texture processing capabilities of the pre-trained RGB model into HSI while keeping spectral fidelity, 2) learning in the spectral-decorrelated domain can improve the generalizability to spectral-agnostic data, and 3) our inference in the eigenimage domain naturally exploits the spectral low-rank property of HSI, thereby reducing the complexity. This work bridges the gap between pre-trained RGB models and HSI via eigenimages, addressing the issue of limited HSI training data, hence the name EigenSR. Extensive experiments show that EigenSR outperforms the state-of-the-art (SOTA) methods in both spatial and spectral metrics. Our code will be released.